7/5X=1,25x

Solution for 7/5X=1,25x equation:

7/5X=1.25X

We move all terms to the left:

7/5X-(1.25X)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We add all the numbers together, and all the variables

7/5X-(+1.25X)=0

We get rid of parentheses

7/5X-1.25X=0

We multiply all the terms by the denominator


-(1.25X)*5X+7=0

We add all the numbers together, and all the variables

-(+1.25X)*5X+7=0

We multiply parentheses

-5X^2+7=0

a = -5; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-5)·7
Δ = 140
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*-5}=\frac{0-2\sqrt{35}}{-10}
=-\frac{2\sqrt{35}}{-10}
=-\frac{\sqrt{35}}{-5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*-5}=\frac{0+2\sqrt{35}}{-10}
=\frac{2\sqrt{35}}{-10}
=\frac{\sqrt{35}}{-5}
$